Use the formula for the sum of the first n terms of an arithmetic series to find the sum of the first eleven terms of the arithmetic series 2.5, 4, 5.5, … .

Expert Solution

Consider the arithmetic sequence,

2.5, 5, 5.5, …

First term of the sequence is a1 = 2.5

Compute common difference as follows:

d = a2 – a1

= 4 – 2.5

= 1.5

Use the formula for nth term of an arithmetic sequence,

an = a1 + (n – 1)d ...... (1)

Substitute a1 = 2.5, d = 1.5 and n = 11 in formula (1) and compute 11th term of the sequence,

a11 = 2.5 + (11 – 1) × 1.5

= 2.5 + 10 × 1.5

= 2.5 + 15

= 17.5

Use the formula for the sum of first n terms of an arithmetic sequence,

Sn = n(a1 + an)/2 ...... (2)

Substitute a1 = 2.5, an = 17.5 and n = 11 in formula (2) and simplify,

S11 = 11(2.5 + 17.5)/2

= 11 × 20/2

= 110

Junaid answered 1 year ago

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